Representations of the Quantum Algebras U q (su(2)) and U q (su(1,1))

Abstract

Quantum Groups and Algebras made their appearance in the quantum methodical treatment of the inverse scattering problem [1–3]. Presently the representation theory for the quantum groups and algebras is being actively and vigorously pursued. The results to be obtained are of considerable interest to quantum field theory as well as to statistical physics [4]. Recent papers [5–9] also show that representations of quantum groups and algebras are closely related to the so-called basic hypergeometric functions.